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Optional decomposition of supermartingales and hedging contingent claims in incomplete security markets

Kramkov, D.O. - University of Bonn, Germany - 1994

Let M(X) be a family of all equivalent local martingale measures for some locally bounded d-dimensional process X, and V be a positive process. Main result of the paper (Theorem 2.1) states that the process V is a supermartingale whatever Q in M(X), if and only if this process admits the...

Persistent link: https://www.econbiz.de/10004968206

On Smile and Skewness

Platen, Eckhard; Schweizer, Martin - University of Bonn, Germany - 1994

This paper proposes a new explanation for the smile and skewness effects in implied volatilities. Starting from a microeconomic equilibrium approach, we develop a diffusion model for stock prices explicitly incorporating the technical demand induced by hedging strategies. This leads to a...

Persistent link: https://www.econbiz.de/10004968203

A Market Model for Stochastic Implied Volatility

Schönbucher, Philpp J. - University of Bonn, Germany

implied Black-Scholes volatilities of a set of given standard options. Thus the model is able to capture the stochastic …

Persistent link: https://www.econbiz.de/10004968281

On the Approximation of Random Variables by Stochastic Integrals with Respect to Semimartingales

Christopeit, Norbert - University of Bonn, Germany - 1994

In this paper it is shown that the space of stochastic integrals w.r. to a special semimartingal is closed and hence every square integrable random variable admits a best approximation in this space. In terms of financial economics this means that for every contingent claim there exists a...

Persistent link: https://www.econbiz.de/10005085669

Continuous-Time Term Structure Models

Musiela, Marek; Rutkowski, Marek - University of Bonn, Germany - 1996

pagehe problem of term structure of interest rates modelling is considered in a continuous-time framework. The emphasis is on the bond prices, forward bond prices or LIBOR rates, rather than on the instantaneous rates as in the traditional models. Forward and spot probability measures are...

Persistent link: https://www.econbiz.de/10005085674

The Stochastic Finite Element Method and Application in Option Pricing

Look, Stefan - University of Bonn, Germany

The purpose of this paper is to present a numerical method to solve partial stochastic differential equations. This concept remains the differential operator unchanged but discretizes the dimension of the problem. The response function will be decomposed by the Karhunen--Loeve expansion and...

Persistent link: https://www.econbiz.de/10005032148

Pricing and Hedging of Contingent Claims in Term Structure Models with Exogenous Issuing of New Bonds

Sommer, Daniel - University of Bonn, Germany - 1997

If calibrated to an observed term structure of interest rates that only covers a finite range of times-to-maturity an HJM-model of the term structure of interest rates will eventually die out in finite time as bonds reach maturity. This poses problems for the pricing and hedging of certain...

Persistent link: https://www.econbiz.de/10005032167

A Term Structure Model and the Pricing of Interest Rate Derivative

Sandmann, K.; Sondermann, D. - University of Bonn, Germany - 1993

support is derived for the spot rate return. The model permits the arbitrage free valuation of bond options and interest rate … options and produces dynamic portfolio strategies to duplicate these contracts. …

Persistent link: https://www.econbiz.de/10005032172

A Discrete Time Approach for European and American Barrier Options

Sandmann, K.; Reimer, M. - University of Bonn, Germany - 1995

The extension of the Black-Scholes option pricing theory to the valuation of barrier options is reconsidered. Working … in the binomial framework of CRR we show how various types of barrier options can be priced either by backward induction …, the case of American barrier options is analyzed in detail. For American barrier call options, binomial formulae and their …

Persistent link: https://www.econbiz.de/10005032188

Robustness of Gaussian Hedges and the Hedging of Fixed Income Derivatives

Dudenhausen, Antje; Schloegl, Erik; Schloegl, Lutz - University of Bonn, Germany - 1999

The effect of model and parameter misspecification on the effectiveness of Gaussian hedging strategies for derivative financial instruments is analyzed, showing that Gaussian hedges in the `natural'' hedging instruments are particularly robust. This is true for all models that imply...

Persistent link: https://www.econbiz.de/10004989597